Method and apparatus for determining wave characteristics using interaction with a known wave

Abstract

The described system and method uses data from interaction between a known wave and an unknown wave to analyze or characterize the unknown wave using cross correlation frequency resolved optical gating (X-FROG). The system may obtain X-FROG trace data from the interaction between the two waves. The system analyzes the X-FROG trace data using a modified principal component generalized projection method strategy to invert the X-FROG trace data, analyzing or characterizing the unknown wave. Results of the analysis can be provided in real time and displayed.

What is claimed is: 
     
       1. A method for determining characteristics of a first electromagnetic wave, the method comprising:
 providing a relative shift between a first electromagnetic wave and a second electromagnetic wave, the relative shift controlled to provide a sequence of shifts between the first electromagnetic wave and the second electromagnetic wave; 
 multiplying the first electromagnetic wave with the second electromagnetic wave following each of the sequence of shifts to provide a sequence of multiplied output electromagnetic waves; 
 measuring, by an electronic detector coupled to a digital computer, an intensity for each of the sequence of multiplied output electromagnetic waves to provide a sequence of detected wave values as detected wave phenomena data; 
 generating, by a processor of the digital computer, generated wave phenomena data based on a reversible transform of a product of at least first and second generated waves, the second generated wave based on known information about the second electromagnetic wave; and 
 determining, by the processor of the digital computer, characteristics of the first electromagnetic wave from the generated wave phenomena data by applying the detected wave phenomena data as a constraint to the generated wave phenomena data to develop a projection operator, applying the projection operator to one of the first or second generated waves to project the one of the first or second generated waves into a space of the other of the first or second generated waves to provide an estimate of the other of the first or second generated waves, and generating further generated wave phenomena data using the estimate. 
 
     
     
       2. The method according to  claim 1  wherein the determining comprises using principal component general projections. 
     
     
       3. The method according to  claim 1  wherein the determining comprises solving for an unknown singular vector using a power method. 
     
     
       4. The method according to  claim 1  wherein the determining comprises projecting the second generated wave onto the first generated wave. 
     
     
       5. The method according to  claim 4  wherein the projecting uses the power method. 
     
     
       6. The method according to  claim 1  wherein the determining comprises projecting the first generated wave onto the second generated wave. 
     
     
       7. The method according to  claim 1  wherein the relative shift is a phase shift, a temporal shift or a spatial shift. 
     
     
       8. The method according to  claim 1  wherein the multiplying comprises second harmonic generation, third harmonic generation, polarization gating or self-diffraction. 
     
     
       9. The method according to  claim 1  further comprising displaying aspects of the first electromagnetic wave based on the characteristics of the first electromagnetic wave. 
     
     
       10. The method according to  claim 9  wherein the method performs frequency resolved optical gating and wherein the wave phenomenon is a spectrogram. 
     
     
       11. The method according to  claim 10  further comprising displaying the spectrogram. 
     
     
       12. The method according to  claim 11  wherein the relative shift is a phase shift, a temporal shift or a spatial shift. 
     
     
       13. The method according to  claim 10  further comprising displaying aspects of the first electromagnetic wave based on the characteristics of the first electromagnetic wave. 
     
     
       14. The method according to  claim 9  wherein the determining comprises projecting the second generated wave onto the first generated wave. 
     
     
       15. The method according to  claim 9  wherein the determining comprises projecting the first generated wave onto the second generated wave. 
     
     
       16. The method according to  claim 9  wherein the multiplier is a second harmonic generation material, the wave phenomena data is detected by a spectrometer and the wave phenomena data is a spectrogram. 
     
     
       17. The method according to  claim 1  further comprising:
 generating the first electromagnetic wave by reflecting or refracting an input wave off an object so that characteristics of the object modulate the input wave, wherein the relative shift is a spatial shift; and 
 displaying aspects of the object by processing the first electromagnetic wave. 
 
     
     
       18. The method according to  claim 1  wherein the multiplying is performed by a multiplier, the wave phenomena data is detected by a spectrometer and further comprising displaying aspects of the first electromagnetic wave based on the characteristics of the first electromagnetic wave. 
     
     
       19. The method according to  claim 18  wherein the multiplier is a nonlinear material. 
     
     
       20. The method according to  claim 18  wherein the wave phenomena data is a spectrogram. 
     
     
       21. A method for determining characteristics of a first electromagnetic wave, the method comprising:
 providing a relative shift between a first electromagnetic wave and a second electromagnetic wave, the relative shift controlled to provide a sequence of shifts between the first electromagnetic wave and the second electromagnetic wave; 
 multiplying the first electromagnetic wave with the second electromagnetic wave following each of the sequence of shifts to provide a sequence of multiplied output electromagnetic waves; 
 measuring, by an electronic detector coupled to a digital computer, an intensity for each of the sequence of multiplied output electromagnetic waves to provide a sequence of detected wave values as detected wave phenomena data; 
 generating, by a processor of the digital computer, generated wave phenomena data based on a reversible transform of a product of at least first and second generated waves, the second generated wave based on known information about the second electromagnetic wave; 
 determining, by the processor of the digital computer, characteristics of the first electromagnetic wave from the generated wave phenomena data by applying the detected wave phenomena data as a constraint to the generated wave phenomena data to develop a projection operator, applying the projection operator to the first generated wave to project the first generated wave into a space of the second generated wave to provide an estimate of the second generated wave, and generating further generated wave phenomena data using the estimate. 
 
     
     
       22. The method according to  claim 21  further comprising displaying aspects of the first electromagnetic wave based on the characteristics of the first electromagnetic wave. 
     
     
       23. The method according to  claim 22  wherein the further generated wave phenomena data is generated using the projected first generated wave and the known information about the second electromagnetic wave. 
     
     
       24. The method according to  claim 23  wherein the relative shift is a phase shift, a temporal shift or a spatial shift. 
     
     
       25. The method according to  claim 23  wherein the multiplying comprises second harmonic generation, third harmonic generation, polarization gating or self-diffraction. 
     
     
       26. The method according to  claim 25  wherein the multiplying is performed by a second harmonic generation material or a third harmonic generation material. 
     
     
       27. The method of  claim 25  wherein the method performs frequency resolved optical gating and the wave phenomena data is detected by a spectrometer.